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The graph of a polynomial function of degree 5 has three x-intercepts, all with multiplicity 1. Describe the nature and number of all its zeros.

Final answer:

A baker would need to use 7 scoops of flour with a 1 1⁄2 cup measuring scoop to have at least 4 3⁄4 cups of flour.

Explanation:

The question at hand requires us to determine how many scoops of flour a baker would need to use to obtain at least 4 3⁄4 cups of flour with a scoop that holds 1 1⁄2 cups. To solve this, we will divide the total amount of flour needed by the capacity of the scoop:

Therefore, the baker must use 7 scoops to have at least 4 3⁄4 cups of flour.

Answer:

See below.

Step-by-step explanation:

The 2 functions have the same output value when x = 7  ( that is what m(x) = p(x) at x = 7 means).

Answer:

51

Step-by-step explanation:

Given

P(x) = 2x³ + 4x² - 10x - 9, then

P(a) = 2a³ + 4a² - 10a - 9 ← substitute x = a into P(x)

To evaluate P(3) substitute a = 3 into P(a)

P(3) = 2(3)³ + 4(3)² - 10(3) - 9 = 54 + 36 - 30 - 9 = 51

Since P(3) ≠ 0 then (x + 3) is not a factor of P(x)

Answer:

51

Step-by-step explanation:

2(3)³ + 4(3)² - 10(3) - 9

= 51

Answer: $965

Step-by-step explanation:

The used car is priced at $2,695.

If you borrow the money for the car, your payments will be $122 a month for 30 months. This means that the total amount of money that you would have paid at the end of 30 months at a rate of $122 per month is the amount paid per month multiplied by the total number of months. It becomes

Total payment = 122×30 = $3660

This means that you ended up paying higher than you would have paid if you paid cash.

Amount that you would have saved = amount paid over 30 months - cost of the car

Amount that you would have saved

= 3660 - 2695 = $965

By paying cash for the used car priced at $2,695, you will save $965. Option C is correct.

The total amount paid when financing the car can be found by multiplying the monthly payment by the number of months:

Total amount paid when financing = Monthly payment × Number of months

= $122 × 30

= $3,660

To find the savings, we subtract the total amount paid when financing from the total cost of the car when paying cash:

Savings = Total cost of the car when paying cash - Total amount paid when financing

= $2,695 - $3,660

= -$965

Since the result is negative, it means you would actually be paying more when financing the car compared to paying cash.

Absolute value of savings = |- $965|

= $965

Therefore, the correct answer is  $965.

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CCCCCCCCCCCCCCCCCCCCCC

Answer:

The correct answer is option "C"

"The interquartile range increases"

The value of the (RIC) will increase from 4 to 5.75, that is, 44%

Step-by-step explanation:

The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin

The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.

Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%

Answer:

Option C. w=5×15

Step-by-step explanation:

Let

w ----> the amount of dollars to buy 5 tickets

we know that

The variable w is equal to multiply the numbers of tickets by the cost of each ticket

so

The equation that represent this situation is

w=5(15)

Answer:

Thus, the required equation is W=15×5

Step-by-step explanation:

Consider the provided information.

Gina wants to go to the water park with her friends. They have a total of w dollars.

W represents the total money they have.

They buy 5 tickets and each ticket cost 15 dollars.

Thus the total cost for 5 tickets is:

15×5

She had W dollars. That means the above expression is equal to W.

W=15×5

Thus, the required equation is W=15×5.

(3√-3)(3√-5)  multiply 3 and 3, and multiply √-3 and √-5 together, the √ stays

9√15   Your answer is A

Answer:

The correct answer is option A.  9 √15

Step-by-step explanation:

It is given that, 3√-3 and 3 √-5

To find the product

we have, 3√-3 and 3 √-5

(3√-3) * (3 √-5) = 3√-3 * 3 √-5

 = (3 * 3) (√-3 * √-5)

 = 9 * √(-3 * -5)

 = 9* √15

 = 9√15

Therefore the correct answer is option A.  9√15

Answer:

C. 3 in x 6 in

Step-by-step explanation:

Jammal cuts the block in a straight line parallel to one side... so the section revealed when he finishes his cut will be identical as the parallel side to which the cut is done.

We know the the left side of the prism on the image is 3 inches wide and 6 inches high... so that will also be the dimensions of the exposed cross section.

The answer is then 3 inches y 6 inches. The thickness of the block (5 inches) has no impact on the exposed area of the cross-section.

Answer:

4:The denominator can't be equal to 0, therefore -  5

5: 4)The denominator can't equal to 0 -4

Answer:

Question 4:

(x² - 25) / (x - 5)

= (x² - 5²) / (x - 5)

= [(x - 5) · (x + 5)] / (x - 5)

= x + 5

The denominator can't be equal to 0, therefore:

x - 5 ≠ 0 ⇔ x ≠ 5

Question 5:

(3x² - 6x) / (x² - 2x - 8)

= [3x (x - 2)] / (x² + 4x - 2x - 8)

= [3x (x - 2)] / [x (x + 4) - 2 (x + 4)]

= [3x (x - 2)] / [(x - 2) (x + 4)]

= 3x / (x + 4)

The denominator can't equal to 0, therefore:

x + 4 ≠ 0 ⇔ x ≠ -4

Answer:

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3

Step-by-step explanation:

The expansion of the given (4x – 2)(2x 2 + 3) is

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3.

We have given that the (4x – 2)(2x 2 + 3)

We have to determine the expansion of the(4x – 2)(2x 2 + 3)

the act of expanding or the state of being expanded · something expanded; an expanded surface or part · the degree, extent, or amount by which something expands.

Therefore the expansion is given by

[tex](4x -2)(2x^ 2 + 3)=4x*2x^2+4x*3+(-2)*2x^2+(-2)*3[/tex]

Therefore we get the expansion of the given (4x – 2)(2x 2 + 3) is

4x*2x^2+4x*3+(-2)*2x^2+(-2)*3.

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Answer:

1/2

Step-by-step explanation:

see the picture.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

cosx = [tex]\sqrt{1-sin^2x}[/tex]

note that ([tex]\frac{\sqrt{3} }{2}[/tex] )² = [tex]\frac{3}{4}[/tex]

cosΘ = [tex]\sqrt{1-\frac{3}{4} }[/tex] = [tex]\sqrt{\frac{1}{4} }[/tex] = [tex]\frac{1}{2}[/tex]

ANSWER

There are 210 different permutations

EXPLANATION

The word 'ALFALFA' has 7 letters.

The letter 'A' repeats three times.

The letter 'F' repeats two times.

The letter 'L' also repeats two times.

The number of different permutation is

[tex] \frac{7!}{3!2!2!} = 210[/tex]

There are 210 different permutations.

Answer: There are 210 distinct permutations of the letter of that word.

Step-by-step explanation:

Since we have given that

ALFALFA

Here, 3 A,

2 F,

2 L

Number of letters in that word = 7

So, Number of distinct permutations of the letters of the word "ALFALFA":

[tex]\dfrac{7!}{3!\times 2!\times 2!}\\\\=210[/tex]

Hence, there are 210 distinct permutations of the letter of that word.

radius=diameter/2

therefore r=3÷2 ie 1.5m

area=pi (r^2)m^2

=1.5^2 pi m^2

2.25 pi m^2 is required area

Answer:

16

Step-by-step explanation:

128 stamps and 8 pages have the same amount to add up to 128

So 128 ÷ 8 I'll make it easier

8÷8=1

40÷8=5

80÷8=10

(128÷8)

10+5+1 = 16

There are 16 stamps per page.

Answer:

16 stamps.

Step-by-step explanation:

128 stamps divided by 8 stamps per page is 16 stamps.

Answer:

B

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

To obtain this form use the method of completing the square

Given

x² - 8x + y² - 2y - 8 = 0 ( add 8 to both sides )

x² - 8x + y² - 2y = 8

add ( half the coefficient of the x/y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 8 + 16 + 1

(x - 4)² + (y - 1)² = 25 → B

Final answer:

The standard form of the given circle equation is (x - 4)^2 + (y - 1)^2 = 25, which is option (B).

Explanation:

To rewrite the given equation of a circle in standard form, we need to complete the square for both x and y terms. The equation is given as:

x² − 8x + y² - 2y - 8 = 0

We organize the equation by grouping x and y terms:

(x² − 8x) + (y ² - 2y ) = 8

To complete the square, we add to each side (½ the coefficient of x) ² for the x-terms and (½ the coefficient of y) ² for the y-terms:

For the x terms: (½ × -8)² = (-4)² = 16. Add 16 to both sides.

For the y terms: (½ × -2)² = (-1)² = 1. Add 1 to both sides.

Our equation becomes:

(x² − 8x + 16) + (y² - 2y + 1) = 8 + 16 + 1

Which simplifies to:

(x - 4)² + (y - 1)² = 25

Therefore, the standard form of the given equation is (x - 4)² + (y - 1)² = 25, and the correct answer from the options is (B).

Answer:

[tex](-\frac{3}{8},2)[/tex]

Step-by-step explanation:

Point Z divides XY into a 5:3 ratio, so Z is 5/3 of the way from X to Y.  That ratio is k, found by writing the numerator of the ratio (5) over the sum of the numerator and the denominator (5 + 3 = 8).  Our k value is 5/8.  Now we will find the rise and run values which is the slope of this line segment:

[tex]m=\frac{2-2}{-6-9} =\frac{0}{-15}[/tex]

Coordinates are found in this formula:

[tex]Z(x,y)=(x_{1}+k(run),y_{1} +k(rise))[/tex]

Filling that in:

[tex]Z(x,y)=(9+\frac{5}{8}(-15),2+\frac{5}{8}(0))[/tex]

which simplifies to

[tex]Z(x,y)=(9-\frac{75}{8},2+0)[/tex]

which gives us the final coordinates of Z to be [tex]Z(x,y)=(-\frac{3}{8},2)[/tex]

Answer:

I think it's the last one, BD/AE

Step-by-step explanation:

To find the sum of the x-coordinates of all possible positive integer solutions to the equation 1/x + 1/y = 1/7, we can rearrange the equation and use Simon's Favorite Factoring Trick to solve for x.

To find the sum of the x-coordinates of all possible positive integer solutions to the equation 1/x + 1/y = 1/7, we can rearrange the equation to 7x + 7y = xy. Simplifying further, we have xy - 7x - 7y = 0. Applying Simon's Favorite Factoring Trick, we add 49 to both sides of the equation: xy - 7x - 7y + 49 = 49. Factoring the left side gives us (x - 7)(y - 7) = 49. Since we are looking for positive integer solutions, we can set x - 7 and y - 7 to be divisors of 49 and solve for x.

The divisors of 49 are 1, 7, and 49. Setting x - 7 = 1, we get x = 8. Setting x - 7 = 7, we get x = 14. And setting x - 7 = 49, we get x = 56. So the sum of the x-coordinates is 8 + 14 + 56 = 78.

Answer the answer is c

Step-by-step explanation:

I also got C for this answer

They left the park at 3:05

Answer:

F. (0, 5) and (-4, 2)

Step-by-step explanation:

We need to calculate the slope of each of the given sets of points until we find the set associated with a slope of 3/4:

F. (0,5) and (-4,2)  As we go from (-4, 2) to (0,5), x increases by 4 and y increases by 3, so the slope is m = rise / run = 3/4.  This is the line with slope 3/4.

Answer A becaus descriminant =16-4*3*2=-8

ANSWER

A. There are two complex roots.

EXPLANATION

The given quadratic equation is

[tex]3x^2+4x+2=0[/tex]

when we compare this to

[tex]a {x}^{2} + bx + c = 0[/tex]

we have a=3,b=4 and c=2.

We use the discriminant to determine the nature of roots.

[tex]D= {b}^{2} -4ac [/tex]

[tex]D= {4}^{2} -4(3)(2) [/tex]

[tex]D= 16-24[/tex]

[tex]D= - 8[/tex]

Since the discriminant is less than zero, the equation will have 2 complex roots.

Answer:

The line x = 8 is our vertical asymptote

The limit of [tex]\frac{1}{x-8}[/tex] as x approaches 8 from the left is negative infinity; -∞

Step-by-step explanation:

We have been given the following function;

[tex]\frac{1}{x-8}[/tex]

Considering that the function is rational, it will defined everywhere on the real line except where the expression in the denominator will be 0;

That is the function will not be defined where;

x - 8 = 0

solving for x yields;

x = 8

The function will be approaching the vertical line x = 8 asymptotically, meaning that the function will never touch or cross this line. We can therefore say that,

The line x = 8 is our vertical asymptote for the given function

The limit of [tex]\frac{1}{x-8}[/tex] as x approaches 8 from the left;

[tex]\lim_{x \to8^{-} }\frac{1}{x-8}[/tex]

For x approaching 8 from the left, [tex]x<8[/tex] which implies that [tex]x-8<0[/tex]

The denominator will be a negative quantity approaching 0 from the left, that is -∞.

Thus;

[tex]\lim_{x \to8^{-} }\frac{1}{x-8}[/tex] = -∞

Find the graph attached.

Answer:

it goe towards negative infinity

Step-by-step explanation:

1/6-8=-1/2

1/7-8=-1

1-7.999-8=-10000

therefore you can assume that it is going to a negative infinity direction

Ethan's car used 6 gallons of gasoline for his 180 miles trip, which at a cost of $4 per gallon, results in a total gasoline cost of $24.

To calculate the total cost of gasoline for Ethan's trip, you need to understand how many gallons were used and then multiply that figure by the cost per gallon. As Ethan's car can travel 30 miles per gallon, and Ethan drove 180 miles in total, Ethan's car used 6 gallons of gasoline (180 miles ÷ 30 miles/gallon). Given that gasoline costs $4 per gallon including tax, Ethan therefore spent a total of $24 on gasoline for his trip (6 gallons x $4/gallon).

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The cost per gallon is $24.

To calculate the total cost of the gasoline, we need to divide the distance driven by the car by the car's gas mileage to find the number of gallons used.

Then, we can multiply the number of gallons used by the cost per gallon to find the total cost. In this case,

Ethan drove 180 miles and his car can travel 30 miles per gallon, so he used 180/30 = 6 gallons of gasoline.

The cost per gallon is $4, so the total cost is 6 * $4 = $24.

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Answer:

A. -25° 29' 24"

Step-by-step explanation:

It is easier to talk about this by considering the magnitude of the angle, then applying the sign to the result.

The fractional part, 0.49°, can be multiplied by 60' per degree to get the number of minutes:

0.49° × 60'/1° = 29.4'

The fractional part of this, 0.4', can be multiplied by 60" per minute to get the number of seconds:

0.4' × 60"/1' = 24"

Then the angle is ...

-25.49° = -25° 29' 24"

_____

Alternate solution

You can recognize this is 0.01° less than 25° 30', so is ...

0.01° × 60' = 0.6' = 0.6 × 60" = 36"

When 36" is subtracted from 25.5° = 25° 30', the result is 25° 29' 24". Of course, your angle is negative: -25° 29' 24".

_____

Comment on base-60 arithmetic

In base-10 arithmetic, when you borrow 1 from the next higher place in the number, you are borrowing ten of the current place. For example, when you are doing arithmetic with hundreds, and you borrow 1 from the thousands place, you have effectively borrowed 10 hundreds.

In base-60 arithmetic, when you borrow one from the next higher place, you borrow 60 of the current unit. That is, borrowing one minute gives you 60 seconds. Thus, 30 minutes is the same as 29 minutes and 60 seconds. Subtracting 36 seconds from this value gives 29 minutes and 24 seconds.

The term "borrowing" was used when I learned arithmetic. More recently, I've seen it called "rewriting" the number. I also think of it as "making change": changing a higher unit to an equivalent number of smaller units.

Answer:

[tex]y=0.2x+3[/tex]

Step-by-step explanation:

Let

x ----> the number of stickers

y ----> the price of the boxes

we have the points

[tex]A(15,6),B(25,8)[/tex]

Find the slope

[tex]m=(8-6)/(25-15)[/tex]

[tex]m=2/10=0.20[/tex]

Find the equation of the line into point slope form

The equation is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute the value of m and the point A

[tex]y-6=0.2(x-15)[/tex]

[tex]y=0.2x-3+6[/tex]

[tex]y=0.2x+3[/tex] ----> linear equation that represent the situation

Answer:

Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference.

Step-by-step explanation:

The result of subtracting two or more numbers in mathematics is called the difference. In vector subtraction, this applies as we add the first vector to negative of the vector that needs to be subtracted, resulting in a difference vector. This is equivalent to subtracting scalar values.

In mathematics, the result of subtracting two or more numbers is known as the difference. This concept also applies to vectors in a process called Vector Subtraction.

For instance, if we have two vectors A and B, and we wish to subtract B from A (usually written as A - B), we do so by adding the first vector, A, to the negative (-) of the second vector, B (written as A + (-B)). Here, -B (negative B) represents the same vector as B but in the opposite direction. The subtraction of A and B results in a difference vector, D, i.e., D = A - B.

The same principle is true for ordinary numbers. Take the numbers 5 and 2 for example. If we subtract 2 from 5 (5 - 2), it's equivalent to adding 5 and -2 (5 + (-2)). Here, the difference is 3.

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Answer:

660

Step-by-step explanation:

Because the ration is 1:5, then 132 chaperones times 5 is 660 students. Please like me and rate!!

The calculated area of the triangle is 18 square units

How to calculate the area of the triangle in square units?

From the question, we have the following parameters that can be used in our computation:

(–2, –1), (4, –1), (6, 5)

The area of the triangle in square units is calculated as

Area = 1/2 * |x₁y₂ - x₂y₁ + x₂y₃ - x₃y₂ + x₃y₁ - x₁y₃|

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * |-2 * -1 - 4 * -1 + 4 * 5 - 6 * -1 + 6 * -1 - 5 * -2|

Evaluate the sum and the difference of products

Area = 1/2 * 36

So, we have

Area = 18

Hence, the area is 18 square units

Answer:

2.78

Step-by-step explanation:

We are given the expression [tex]x^2-1.78x[/tex]

As we know that x=2.78, we can plug that value into the expression and simplify it

[tex](2.78)^2-1.78(2.78)\\\\7.7284-4.9484\\\\2.78[/tex]